Răspuns:
Explicație pas cu pas:
a) f=x²(x - 1)³(2x - 1)⁴
x=0 radacina dubla
x=1 radacina tripla
x=1/2 radacina cvadrupla
b) f=x²(x²-x)³(x²-1)² =x³(x-1)(x-1)(x+1)=x³(x-1)²(x+1)
x=0 radacina tripla
x=1 radacina dubla
x=-1 radacina simpla
c) f= (x²-x-2)²(2x²-3x+1)³(x²-1)²
x²-x-2=0
x1,2=1±√1+8/2=1±3/2 x1=2 x2=-1 ⇒ x²-x-2=(x+1)(x-2)
2x²-3x+1=0
x1,2=3±√9-8/4=3±1/4 x1=1 x2=1/2
2x²-3x+1=(x-1)(2x-1)
f(x)= (x²-x-2)²(2x²-3x+1)³(x²-1)²=(x+1)²(x-2)²(x-1)³(2x-1)³(x-1)(x+1)=
=(x+1)³·(x-1)^4·(x-2)²(2x-1)³
x=1 radacina cvadrupla
x=-1 radacina tripla
x=2 radacina dubla
x=1/2 radacina tripla